Dissertations and Theses

12-2014

Design and Dynamic Analysis of a Variable-Sweep, Variable-Span Morphing UAV

Nirmit Prabhakar Embry-Riddle Aeronautical University - Daytona Beach

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DESIGN AND DYNAMIC ANALYSIS OF A VARIABLE SWEEP, VARIABLE SPAN MORPHING UAV

By

Nirmit Prabhakar

A Thesis Submitted to the College of Engineering Department of Aerospace Engineering in Partial Fulfillment of the Requirements for the Degree of Master of Science in Aerospace Engineering

Embry-Riddle Aeronautical University Daytona Beach, Florida December 2014

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Dedication

To my Grandfather and Grandmother, For shaping me into the person I’m today.

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Acknowledgements

It gives me pleasure to acknowledge the following people for all the support and strength they gave me, which helped make this thesis possible:

I would like to thank Dr. Richard J Prazenica and for the guidance, supervision, and patience he has shown to and with me for the last year and a half. I’d like to thank

Prof. Snorri Gudmundsson for sharing his innovative ideas with me and helping me with the technical aspects of this thesis. I would like to show my gratitude for both my advisors for motivating me to achieve my potential and making me realize the importance of integrity of research.

I would like to thank Dr. Ebenezer Gnanamanickam for all his advice and suggestions regarding the design and implementation of the experimental part of this thesis.

I would like to share this achievement with my mother Dr. Manju Prabhakar, my father Vinod Prabhakar and my sister Bhavya and thank them for their love, motivation, support and faith in me.

I would like to express deep appreciation towards my friends Sadaf Meghani and

William Morgan for their support and encouragement throughout my thesis work.

Finally, I would like to thank everyone at EFRC and FDCRL, my team for Design

Build and Test, and all my friends and my relatives for all the support they have shown during this time.

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Abstract

Researcher: Nirmit Prabhakar

Title: Design and Dynamic Analysis of a Variable-Sweep, Variable-Span

Morphing UAV

Institution: Embry-Riddle Aeronautical University

Degree: Master of Science in Aerospace Engineering

Year: 2014

Morphing wings have the potential to optimize UAV performance for a variety of flight conditions and maneuvers. The ability to vary both the wing sweep and span can enable maximum performance for a diverse range of flight regimes. For example, low- speed missions can be optimized using a wing with high aspect ratio and no wing sweep whereas high-speed missions are optimized with low aspect ratio wings and large wing sweep. Different static morphing wing configurations clearly result in varying aerodynamics and, as a result, varying dynamic modes. Another important consideration, however, is the transient dynamics that occur when transitioning between morphing configurations, which is clearly a function of the rate of transition. For smaller-scale morphing UAVs, morphing transitions can take place on a time scale comparable to the dynamics of the vehicle, which implies that the transient dynamics must be taken into account when modeling the dynamics of such a vehicle.

This thesis considers the dynamic effects of morphing for a variable-sweep, variable-span UAV. A scale model of such a morphing wing has been fabricated and tested in the low-speed wind tunnel at Embry-Riddle Aeronautical University. The focus

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of this thesis is the development of a dynamic model for this morphing wing UAV that accounts for not only the varying dynamics resulting from different static morphing configurations, but also the transient dynamics associated with morphing. A Vortex

Lattice Method (VLM) solver is used to model the aerodynamics of the morphing wing

UAV over a two-dimensional array of static configurations corresponding to varying span and sweep. In this analysis, only symmetric morphing configurations are considered

(i.e., in every configuration, both wings have the same span and sweep); therefore, the analysis focuses on the longitudinal dynamic modes (i.e., the long period and short period modes). The dynamic model of the morphing wing UAV is used to develop a simulation in which it is possible to specify different morphing configurations as well as varying rates of morphing transition. As such, the simulation provides an invaluable tool for analyzing the effects of wing morphing on the longitudinal flight dynamics of a morphing

UAV.

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Table of Contents Dedication ...... iii Acknowledgements ...... iv Abstract ...... v List of Figures ...... ix List of Tables ...... xi CHAPTER 1: INTRODUCTION ...... 1 1.1 MORPHING...... 5 1.1.1 Wing Planform Morphing...... 7 Wing planform morphing ...... 7 1.1.2 Wing Out-of-Plane Transformation...... 7 1.1.3 Airfoil Morphing ...... 9 1.2 TECHNICAL OBJECTIVES...... 11 CHAPTER 2: SURFACES MODEL ...... 12 2.1 MODELING...... 13 2.2 SIMULATION ...... 16 2.3 ANALYSIS ...... 22

2.3.1 CL coefficients ...... 22 2.3.2 CD coefficients ...... 28

2.3.3 Cm coefficients ...... 30 CHAPTER 3: SIMULATION DEVELOPMENT AND CONTROL DESIGN...... 34 3.1 NON-LINEAR SIMULINK MODEL ...... 36 3.2 DYNAMIC MODE ANALYSIS ...... 37 3.3 CONTROLLER DESING...... 43 3.4 SIMULATION RESULTS AND ANALYSIS ...... 45 3.4.1 Open-loop Span change with Zero Sweep...... 46 3.4.2 Open-loop Sweep change with Zero Span increase ...... 49 3.4.3 Open-loop Span and Sweep Morphing ...... 53 3.4.4 Closed Loop Control Cases ...... 56 CHAPTER 4: CONCLUSIONS ...... 58 4.1 Future Scope of Work ...... 60

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APPENDIX A ...... 62 A.1 DESIGN ...... 62 A.2 METHEDOLOGY ...... 65 A.3 RESULTS...... 68 A.3.1 Span Morphing ...... 68 A.3.2 Sweep Morphing ...... 72 A.3.3 Condenser Microphone Results ...... 75 Appendix B ...... 81 Bibliography...... 88

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List of Figures Figure 1.1 Side View of the wing bending in an MAV to achieve Roll control [1]...... 1 Figure 1.2 Gevers Genesis 'tri-phibian' Aircraft [2] ...... 3 Figure 1.3 MFX-1 Morphing Sweep-Span UAV [3]...... 3 Figure 1.4 F-14 Tomcat [5] ...... 4 Figure 1.5 Classification of Wing Morphing [6]...... 6 Figure 1.6 Photo of wing surface showing a steel VSS [16] ...... 9 Figure 1.7 Tip of Experimental Adaptive-Twist airfoil [19] ...... 10 Figure 2.1 SURFACES Model for 10% Span Increase ...... 14 Figure 2.2 SURFACES Model for 10% Span, 30 degree Sweep...... 14 Figure 2.3 CLo trend for Span Change ...... 23 Figure 2.4 CLo trend for Sweep Change...... 23 Figure 2.5 CL trend for Span Change...... 24 Figure 2.6 CL trend for Sweep Change ...... 24 Figure 2.7 CLe trend for Span Change ...... 25 Figure 2.8 CLe trend for Sweep Change ...... 26 Figure 2.9 CLq trend for Span Change ...... 27 Figure 2.10 CLq trend for Sweep Change ...... 27 Figure 2.11 CD trend for Span Change ...... 28 Figure 2.12 CD trend for Sweep Change ...... 29 Figure 2.13 Cm trend for Span Change ...... 30 Figure 2.14 Cm trend for Sweep Change...... 30 Figure 2.15 Cme trend for Span Change ...... 31 Figure 2.16 Cme trend for Sweep Change...... 31 Figure 2.17 Cmq trend for Span Change...... 32 Figure 2.18 Cmq trend for Sweep Change ...... 33 Figure 3.1 Flowchart depicting the flow of the thesis ...... 35 Figure 3.2 Altitude Change for Span Morphing ...... 46 Figure 3.3 Angle of attack change for Span Morphing...... 47 Figure 3.4 Airspeed Change for Span Morphing ...... 47 Figure 3.5 Pitch Rate change for Span Morphing ...... 48 Figure 3.6 Pitch angle change for Span Change ...... 48 Figure 3.7 Altitude Change for Sweep Morphing ...... 50 Figure 3.8 Angle of attack change for Sweep Morphing ...... 51 Figure 3.9 Airspeed change for Sweep Morphing...... 51 Figure 3.10 Pitch Rate change for Sweep Morphing ...... 52 Figure 3.11 Pitch Angle change for Sweep Morphing...... 52 Figure 3.12 Altitude change for Sweep and Span Morphing...... 54 Figure 3.13 Angle of Attack change for Sweep and Span Morphing ...... 54 Figure 3.14 Airspeed change for Sweep and Span Morphing ...... 55 Figure 3.15 Pitch Rate change for Sweep and Span Morphing ...... 55 Figure 3.16 Pitch Angle change for Sweep and Span Morphing ...... 56 Figure 3.17 Altitude Change during controlled Span Morphing...... 57

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Figure 3.18 Altitude Change during controlled Sweep Morphing ...... 57 Figure A.1 Wing Prototype ...... 62 Figure A.2 Hitec-645MG Ultra Torque Servo ...... 65 Figure A.3 Speed/Direction Regulator...... 65 Figure A.4 CCPM servo controller...... 65 Figure A.5 Pressure Transducer/Condenser Microphone Locations ...... 67 Figure A.6 Results of Span Change at 0° AoA Plotted on XFOIL Pressure Distribution ...... 70 Figure A.7 Results of Span Change at 2° AoA Plotted on XFOIL Pressure Distribution ...... 71 Figure A.8 Results of Span Change at 4° AoA Plotted on XFOIL Pressure Distribution ...... 71 Figure A.9 Graphical Representation of Pressure Change for Sweep Change at 0° AoA ...... 73 Figure A.10 Graphical Representation of Pressure Change for Sweep Change at 2° AoA ...... 74 Figure A.11 Graphical Representation of Pressure Change for Sweep Change at 4° AoA ...... 74 Figure A.12 Snap Sweep at 4 Degrees AoA...... 77 Figure A.13 Section of Interest Filtered ...... 78 Figure A.14 PSD of the High-pass and Stop-band filter ...... 78 Figure B.1 Calibration of Pressure Transducer Used at Station 4...... 81 Figure B.2 Calibration of Pressure Transducer Used at Station 7...... 81 Figure B.3 Calibration of Pressure Transducer Used at Station 10 ...... 82 Figure B.4 Electronics...... 82 Figure B.5 XFOIL CP at 0° AoA ...... 84 Figure B.6 XFOIL Pressure Distribution at 0° AoA ...... 85 Figure B.7 XFOIL CP at 2° AoA ...... 85 Figure B.8 XFOIL Pressure Distribution at 2° AoA ...... 86 Figure B.9 XFOIL CP at 4° AoA ...... 86 Figure B.10 XFOIL Pressure Distribution at 4° AoA...... 87

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List of Tables Table 2.1 Surfaces Model Geometry ...... 13 Table 2.2 CL0 Values for various configurations...... 17 Table 2.3 CL values for various configurations ...... 18 Table 2.4 CLq values for various configurations...... 18 Table 2.5 CLe values for various configurations ...... 18 Table 2.6 CD values for various configurations...... 19 Table 2.7 Cm values for various configurations ...... 19 Table 2.8 Cmq values for various configurations ...... 20 Table 2.9 Cme values for various configurations ...... 20 Table 2.10 Comparison between Classical calculations and SURFACES values……….22 Table 3.1 Eigenvalues of the Basic Configuration ...... 41 Table 3.2 Eigenvalues of Full Sweep Configuration ...... 41 Table 3.3 Eigenvalues of Full Span Configuration...... 42 Table 3.4 Eigenvalues of Full Span Full Sweep Configuration...... 42 Table A.1 Change in Coefficient of Pressure from Pre to Post Span Morph ...... 69 Table A.2 Change in Coefficient of Pressure from Pre to Post Sweep Morph...... 72 Table B.1 Pressure Readings from Pre to Post Span Morph ...... 83 Table B.2 Coefficient of Pressure from Pre to Post Span Morph ...... 83 Table B.3 Pressure readings from Pre to Post Sweep Morph ...... 83 Table B.4 Coefficient of Pressure from Pre to Post Sweep Morph ...... 84

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CHAPTER 1: INTRODUCTION

Some of the earliest attempts at flight were aimed at emulating birds and focused in particular on the construction of flapping wing mechanisms. Indeed, birds have evolved into very efficient flying machines, and bio-inspired designs offer many potential benefits for small UAVs. One of the most important and interesting aspects of avian flight dynamics is how birds can change their shape to optimize flight in different conditions. For the most part, these changes take place through morphing of the wings.

Wing morphing in birds can be viewed as an example to optimize aircraft performance over a wider range of conditions. A morphing aircraft can be defined as an aircraft that changes configuration in-flight to maximize its performance at significantly different flight conditions. Since the propulsive power of MAVs is very limited, they stand to benefit from being able to dramatically change their wing geometry in order to accommodate wind gusts and other disturbances.

Figure 1.1 Side View of the wing bending in an MAV to achieve Roll control [1].

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The University of Florida has conducted experiments on the advantages of using bending of the wing (as shown in Figure 1.1) to achieve improved roll control of a MAV

[1]. This morphing MAV featured a faster roll rate and no roll coupling; therefore it was able to achieve better handling qualities. There have been various other aircraft configurations that have used morphing as a way to obtain better performance over a wider flight regime (e.g., Gever’s aircraft [2], MFX-1 [3], etc.). Jha and Kudva [4] outline how a low speed mission requires high aspect ratio and virtually no wing sweep whereas a high speed mission requires the exact opposite. Thus, if an aircraft is developed with the ability to make large configuration changes in an efficient and reversible manner, the same aircraft can fly diversified missions. Jha and Kudva go into further detail on how modifying certain parameters affect aircraft performance. The

MFX-1 [3] concept UAV was developed by Next Gen Aeronautics (Figure 1.3) under a

DARPA project entitled Next Generation Morphing Aircraft Structures (N-MAS). This concept included active morphing of the wing sweep and area to achieve optimal performance over a range of flight conditions.

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Figure 1.2 Gevers Genesis 'tri-phibian' Aircraft [2].

Figure 1.3 MFX-1 Morphing Sweep-Span UAV [3].

Two of the most effective morphing parameters on an aircraft are wing sweep and wing span. For span change, increasing aspect ratio increases lift-to-drag ratio, cruise distance, turn rate, and decreases engine requirements. Decreasing aspect ratio increases the maximum speed and decreases parasitic drag. One example of span change is the telescoping wing on Gever’s aircraft (shown in Figure 1.2), and this is described in more detail on the Gever’s aircraft website [2]. For sweep change, increasing sweep can

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increase the critical Mach number, dihedral effect, and can decrease high speed drag whereas decreasing sweep can increase the maximum lift coefficient. Examples of variable-sweep aircraft include the Messerschmitt, P-1101, Bell X-5, XF101F-1 Jaguar,

F-111 Aardvark and F-14 Tomcat (Figure 1.4). A more in-depth review on the history of morphing aircraft was provided by Barbarino et al. [8].

Figure 1.4 F-14 Tomcat [5].

The technical challenges of morphing discussed by Jha and Kudva [3] include movement of the aerodynamic center and center of gravity during morphing, selecting appropriate materials and designing the structure, reversible actuation without large weight penalties, a skin that maintains optimal aerodynamic performance in pre and post- morphed states and without any gaps, flight control during the transient response of morphing, an engine that performs well for both high and low speeds, and integration of subsystems. Some challenges presented by Barbarino et al. [8] include the additional weight and complexity, power consumption of actuation components, flexible skins that

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remain tight in both pre and post-morphed states, and adequate flight control to handle the changing aerodynamic and inertia characteristics of morphing vehicles.

Even though there has been considerable research done on the performance and aerodynamics of morphing, there has not been much data or analysis on the transient effects of morphing. Barbarino et al. [6], Jha and Kudva [4], and Weisshaar [7] all mention the challenge of developing an adequate flight control to handle the changing aerodynamic and inertia characteristics of morphing vehicles. A recent study was conducted by Grant et al. [8] to analyze the modes of a variable-sweep MAV. The frequency of change of the aerodynamics for this vehicle was of the same magnitude as the rate of change of the wing sweep. Therefore, a linear time-varying (LTV) model was required to properly analyze the morphing dynamics.

This thesis paper is structured as follows. A model of a variable sweep, variable span morphing wing UAV is developed using the software SURFACES [9], which employs the vortex lattice method (VLM) to model the aerodynamics. Using the aerodynamic data resulting from this model, a nonlinear dynamic simulation of this vehicle is then developed in order to simulate the dynamic response to changing the wing span and sweep. Simulation results are presented and the dynamic effects and benefits of morphing are then discussed.

1.1 MORPHING

Morphing can be defined as a transformation from one shape to another. There are various examples around us where morphing can be observed in machines and in nature, from enjoying sunshine in a convertible car on a sunny day to the closing of flower petals

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to prevent pollen from becoming wet and heavy with dew so that insects can easily transfer it [10].

A wing is designed as a compromise in geometry such that aircraft is able to fly at a range of flight conditions, but the performance at each condition is often not optimized or maximum possible efficiency is not obtained. The deployment of conventional flaps or slats on a commercial airplane changes the geometry of its wings; these examples of geometry changes are limited, with narrow benefits compared to those that could be obtained from a wing that is inherently deformable and adaptable. The ability of a wing surface to change its geometry during flight has interested researchers and designers over the years. An adaptive wing diminishes the compromises required to insure operation of the airplane in multiple flight conditions [11]. Aircraft like the F-14 Tomacat or Panavia

Tornado, which apply morphing technology to achieve better performance at both low and high speeds, alleviating the problems of compressibility, are prime examples where the performance benefits have outweighed the structural and weight penalties of morphing. Recent developments in smart materials may overcome these penalties and enhance the benefits of similar design solutions.

Figure 1.5 Classification of Wing Morphing [6].

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Morphing in aircraft has been prevalent since the Wright Flyer, which used wing twist to achieve roll control. New emerging technologies have rendered morphing both more complex and efficient. Geometrical parameters that can be affected by morphing solutions can be categorized into, as seen in Figure 1.5: planform alteration (span, sweep and chord), out-of-plane transformation (twist, dihedral/gull and span-wise bending) and airfoil adjustment (camber and thickness) [6].

1.1.1 Wing Planform Morphing

Wing planform morphing affects three parameters; span, chord and sweep. Span and sweep affect the wing aspect ratio which modifies the lift to drag ratio of the vehicle. An increase in wing aspect ratio would thus result in an increase in range and endurance.

Aerodynamically, change in aspect ratio produces a change in the lift curve slope and forces due to the change in area. Dynamically, the inertias of the aircraft also change.

Chord extensions have been adopted in rotary flights as it is easier (mechanically) to change the chord of a rotor than it is to attempt change of chord on a fixed wing given the structural constrains and the position of fuel tanks in the wings. A study on quasi- statically increasing the chord through the extension of a flat plate on a rotor appeared to give better high lift performances than trailing edge or Gurney flaps [12].

1.1.2 Wing Out-of-Plane Transformation

This is mainly affected by three parameters (individually or in combination): twist dihedral/gull and span-wise bending. Wing aeroelastic twist can be used to produce the required roll moments for control; this can allow the aircraft to operate beyond the

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dynamics pressure limits where aileron reversal would conventionally begin. The

Variable Stiffness Spar (VSS) was developed to vary the torsional stiffness of wings to enhance the roll performance of an aircraft (depicted in Figure 1.6). The concept allows the stiffness and aeroelastic behavior of the wing to be controlled as a function of flight conditions [13]. The VSS concept was further advanced to develop a torsion free wing that allowed for significant aeroelastic amplification to increase the roll rate by 8.44% to

48% above baseline performance. [14]. A wing morphing mechanism was developed in

2005 to vary wing twist to control a swept wing tailless aircraft. Initial wind tunnel tests showed that this mechanism was able to provide adequate forces and moments to control a UAV and potentially a manned aircraft. It also adds the benefit of allowing the aircraft to fly in cruise without the added drag of washout or winglets used to counter the adverse yaw. Tests showed a promising improvement of 15% in the lift to drag ratio when compared to an elevon-equipped wing with built-in 10° washout [15]. A variable dihedral/gull wing has the ability to control the aerodynamic span; replace conventional control surfaces, enhance the agility and flight characteristics of high performance aircraft, reduce induced drag by changing the vorticity distribution and improve stall characteristics [6]. Although out-of-plane morphing is the least common type of morphing solution, recently there has been considerable interest in this method because of the significant impact on the aerodynamic behavior of a control surface without large planform modifications.

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Figure 1.6 Photo of wing surface showing a steel VSS [16].

1.1.3 Airfoil Morphing

Airfoil morphing is the most dominant research topic in morphing methods with more focus being given to camber morphing concepts. The most common method of airfoil morphing is by conventional actuator methods, although with the advent of composites and smart materials, the use of SMA (Shape Memory Alloys), PZT (Piezoelectric materials) and RMA (Rubber Muscle Actuators) has also been studied. The first camber morphing examples stem from the early 1920’s where the wing configuration was changed through the aerodynamic loads on the wing. Wind tunnel tests showed that the wing had a maximum lift coefficient of 0.76 and a minimum drag of 0.007 [17]. Research has also shown that optimal control of the camber can provide an efficient means of improving the L/D ratio at each flight condition during the unsteady phases of periodic optimal endurance cruise and fuel consumption is also minimized during the idle phase

[18]. MAV’s fly at low Reynolds numbers typically in the range of 10,000-100,000; in this region, flow separation on the airfoil can lead to a sudden increase in drag and loss of efficiency. Thus aerodynamic efficiency is critical for MAV design. Active camber

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control can overcome some of the problems of MAV design like flow separation due to low Reynolds number that reduces effectiveness of a trailing edge control surface, elimination/reduction of control surface drag as MAV’s/UAV’s have severe power constraints and an active control surface has the opportunity to provide flow control due to its direct effect on circulation. Example of an Adaptive-Twist airfoil is shown in

Figure 1.7, this model was used to analyze and study active camber changes and their effects on aircraft [19].

Figure 1.7 Tip of Experimental Adaptive-Twist airfoil [19].

Overall it can be argued that, after over a century of flight the aircraft industry has reached a point where the industry can now consider the pursuit of more efficient aircraft configurations that are not optimized to a limited flight regime and purpose. Millions of years of natural evolution have made birds the most efficient flying machines on the planet. Their versatility and ability to adapt to different flight environments and adversities such as wind gusts is unparalleled. Birds have also developed an ability to harvest lift out of nature through thermals and wind shears. Micro Air Vehicles in general lack the propulsive ability to ascend to higher altitudes for loitering and surveillance, and it would be potentially beneficial to program MAVs to utilize thermals and other wind patterns to achieve lift to enhance the endurance of the vehicle. To conceptualize such a system would require a wider range of performance that would be impossible for a MAV if not for morphing. Wing morphing to change the wing geometry would provide a bio-

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inspired scenario for utilization of nature to achieve more efficient lift. With the advent of smart materials the industry is now at a stage where a more intensive study of morphing can be performed without all the weight penalties associated with mechanically morphing the wing and their feasibility can be determined.

1.2 TECHNICAL OBJECTIVES

The design of a morphing wing UAV is developed using the wing test model as a reference. This design is then modeled in SURFACES software [9], which employs the vortex lattice method (VLM) to model the aerodynamics. Using the aerodynamic data resulting from this model, a nonlinear dynamic simulation of this vehicle is then developed in order to simulate the dynamic response to changing the wing span and sweep. Simulation results are presented and the dynamic effects and benefits of morphing are discussed.

In context of this thesis the author will study some changes which take place during morphing and some affects the speed of morphing plays in the dynamics. This will outline the benefits of morphing and provide insight into the dynamic effects of morphing.

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CHAPTER 2: SURFACES MODEL

Classically any airplane preliminary static/dynamic analysis was carried out by either wind tunnel experiments, which are expensive and time consuming, or by the use of statistical estimation methods, which are tedious. With the advent of vortex lattice solvers, aircraft designers have obtained a relatively simple tool that gives them a basic idea of the dynamics of the aircraft without going through the cumbersome process of building a prototype for wind tunnel testing.

The VLM solver used for this research project is called ‘SURFACES’, which is developed and distributed by Flight Level Engineering. SURFACES uses a three- dimensional Vortex Lattice Method (VLM) to determine airflow around the aircraft, allowing the user to extract a large amount of information from the solution ranging from elementary plotting of the flow solution to sophisticated extraction of loads and stability derivatives [9].

A preliminary model is constructed in SURFACES and the geometries and weights are set up. Panels are then defined onto the geometry; these panels have a control volume over which flow is analyzed. The program uses built-in inertia modeling to determine the moments and products of inertias; it also uses the geometry and the defined weight distributions for statistical analysis to determine the neutral point and CG location. Control surfaces and high lift devices such as elevator, rudder, ailerons, flaps, and slats etc. can be incorporated and used to trim the aircraft about the three axes at a

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desirable speed, altitude, CG and power setting. SURFACES uses math objects to determine performance and stability derivatives and automatically computer properties by using model geometry directly, Vortex-Lattice results and others. Force Integrators are used to determine shear and moments about 3-axes on any surface in any orientation and the program can account for thrust, symmetric or asymmetric. [9]

2.1 MODELING

The model created in SURFACES was based on a morphing wing design used for the wind tunnel experiments; a conventional T-Tail configuration was chosen for the design purpose. A preliminary model was created with the set of dimensions given in

Table 2.1.

Table 2.1 Surfaces Model Geometry.

Wing Horizontal Tail Vertical Tail Fuselage 2 S = 3.5ft Bht = 1.5ft Bvt = 0.75ft. L = 4.25 ft. 2 2 C = 1 ft. Sht = 0.75 ft Svt = 0.25ft

This configuration was designated as the 0 Span 0 Sweep base model (Figure 2.1) and then the wings were swept back by an angle of 5 degrees for each configuration while the span was increased by 10% (0.03’) for each configuration, creating a total of 77 different models that conform to the full range of sweep/span configuration that can be achieved by the MAV.

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Neutral Point CG

Figure 2.1 SURFACES Model for 10% Span Increase.

Retention of wing tip after sweep

Moving Servo motor to maintain static margin

Movement of CG and Neutral Point

Figure 2.2 SURFACES Model for 50% Span, 30 degree Sweep.

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One of the most important aspects to consider while designing a morphing aircraft is the neutral point shift that takes place during sweep change. This in turn creates a change in static margin, making it larger as the wings sweep back to a larger angle. This phenomenon would make the aircraft more stable and less maneuverable, hence defeating the purpose of morphing. To counteract this change, a novel mechanism was designed that includes a slider rail in which the servo motors and batteries move in the direction of the sweep (back). This causes the CG to shift back with the Neutral Point making the static margin change less prominent. There is no mechanical way of negating the static margin change apart from compartmentalizing the wing and changing the sweep on the outboard section only, but this would make the mechanism more complicated. Using this mechanism the static margin for all configurations was limited to under or around 15%.

Another matter of concern in this design is the retention of the outboard wing shape after sweeping the wing back (Figure 2.1, 2.2); in a conventional morphing wing the wing tips would no longer be parallel to the oncoming wind and therefore the outboard wing design would have to be modified to incorporate the change. The author realizes the affects that wing tip vortices may cause to the aircraft dynamics but suggests

(even if only theoretically) a design akin to one of a wind shield wiper commonly used in cars with hinged ends to avoid the twisting of the wing tips. This would marginally reduce changes in the tip vortices while simplifying the modeling complexity.

The design and evaluation techniques for large aspect ratio and high Reynolds number fixed wing aircraft are well developed; however vortex lift problems on low

Reynolds number MAVs have made it difficult to extend the same codes. Very little information is available on the performance of existing airfoil/wing shapes at low speeds

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due to this issue. Therefore, extensive wind tunnel testing of the models is necessary to validate any results obtained from computational methods. As the purpose of this thesis is carrying out preliminary analysis and based on the fact that SURFACES provides a very good estimation of the dynamics of the aircraft, the data obtained from the VLM solver are used for the simulation studies presented in this thesis.

2.2 SIMULATION

This thesis work assumes that the stability derivatives change with morphing is a quasi-steady change; this assumption could be verified fairly simply if it can be proven that the frequency of change of the circulation on a wing is much greater than the frequency of the morphing change.

L=ρ∞V∞ Γ b

Where, L = lift generated by the wing

ρ∞ = density of free-stream

V∞ = free-stream velocity

Γ = Circulation

b = span of the wing

The dimensions of Γ are m2/s; hence, if the circulation is multiplied by the cross-sectional area of the wing; frequency of the change can be obtained. Substituting values obtained from the geometry and aerodynamic data from classical calculations we obtain the frequency of circulation to be around 12 hertz, whereas the frequency of change for the

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fastest rate of morphing is an order of magnitude lower than that. Therefore it is safe to assume this to be a quasi-steady system and proceed with the results obtained from

SURFACES.

The models representing the different morphing configurations were estimated according to the Vortex-Lattice Method. SURFACES provide the Aerodynamic center,

CG and the Moment of Inertias calculated on the basis of the geometry of the aircraft model. These values are further used to find the trim conditions, which in turn leads to the calculation of the stability derivatives for the aircraft using classical methods. The results obtained are then classified according to the configurations and different derivatives are graphed with respect to sweep and span in order to identify trends. For the purposes of this study, changes in the longitudinal stability derivatives are considered.

The stability derivatives obtained from SURFACES for all the given configurations are listed below; here the rows indicate different span configurations whereas the columns signify the sweep angles.

Table 2.2 CL0 values for various configurations.

0 10 20 30 40 50 60 70 80 90 100

0 0.161 0.165 0.168 0.170 0.173 0.183 0.188 0.188 0.197 0.202 0.205 5 0.156 0.159 0.160 0.160 0.162 0.164 0.164 0.165 0.167 0.168 0.169 10 0.153 0.155 0.156 0.157 0.158 0.159 0.161 0.162 0.163 0.164 0.165 15 0.148 0.150 0.152 0.152 0.154 0.155 0.155 0.157 0.158 0.159 0.160 20 0.142 0.143 0.144 0.145 0.147 0.148 0.149 0.149 0.151 0.152 0.153 25 0.135 0.136 0.137 0.139 0.140 0.141 0.143 0.143 0.145 0.144 0.147 30 0.126 0.128 0.129 0.130 0.132 0.132 0.134 0.134 0.136 0.137 0.138

CL0 is the coefficient of lift at zero angle of attack, on a CL v/s graphs the slope of the line is represented by CLwhereas the y-axis intercept is known as CLo.

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Table 2.3 CL values for various configurations.

0 10 20 30 40 50 60 70 80 90 100

0 3.962 4.008 4.068 4.109 4.161 4.211 4.313 4.313 4.524 4.628 4.650 5 3.699 3.730 3.755 3.782 3.807 3.833 3.857 3.882 3.908 3.932 3.956 10 3.679 3.710 3.734 3.762 3.786 3.813 3.837 3.862 3.887 3.911 3.935 15 3.638 3.669 3.693 3.720 3.745 3.773 3.795 3.820 3.845 3.870 3.893 20 3.578 3.609 3.632 3.660 3.685 3.704 3.734 3.758 3.782 3.806 3.830 25 3.494 3.526 3.549 3.576 3.596 3.627 3.651 3.675 3.739 3.699 3.757 30 3.386 3.418 3.443 3.471 3.497 3.523 3.547 3.571 3.595 3.618 3.641

Table 2.4 CLq values for various configurations.

0 10 20 30 40 50 60 70 80 90 100

0 7.729 7.822 7.960 7.904 8.048 8.258 8.262 8.262 8.491 8.478 8.268 5 7.752 7.681 7.661 7.614 7.549 7.475 7.439 7.473 7.380 7.380 7.506 10 7.921 7.879 7.810 7.735 7.700 7.730 7.694 7.672 7.614 7.625 7.689 15 8.055 8.021 7.921 7.886 7.823 7.782 7.834 7.782 7.724 7.730 7.826 20 8.217 8.100 7.990 7.979 7.934 7.929 7.875 7.845 7.782 7.749 7.872 25 8.407 8.182 8.148 8.078 8.055 8.014 7.983 7.966 7.929 7.876 7.952 30 8.792 8.623 8.548 8.582 8.416 8.357 8.299 8.258 8.113 8.113 8.190

Table 2.5 CLe values for various configurations.

0 10 20 30 40 50 60 70 80 90 100

0 0.545 0.536 0.526 0.517 0.508 0.547 0.548 0.548 0.548 0.549 0.461 5 0.547 0.537 0.530 0.522 0.514 0.506 0.499 0.491 0.485 0.478 0.471 10 0.552 0.542 0.534 0.526 0.518 0.511 0.503 0.496 0.489 0.482 0.475 15 0.559 0.549 0.541 0.533 0.525 0.518 0.510 0.503 0.496 0.489 0.482 20 0.569 0.559 0.551 0.543 0.535 0.452 0.520 0.513 0.505 0.498 0.492 25 0.578 0.568 0.560 0.551 0.463 0.536 0.528 0.521 0.507 0.514 0.501 30 0.524 0.513 0.506 0.497 0.489 0.484 0.477 0.474 0.467 0.462 0.459

CLq indicates the change in lift with respect to the pitch rate of the aircraft; in terms of aircraft dynamics it represents a pitch damping coefficient. CLe is the change in lift due

18

to the elevator deflection; it represents the control effort of the elevator on the aircraft.

CDcan be represented as the change in drag with respect to the angle of attack of an aircraft.

Table 2.6 CD values for various configurations.

0 10 20 30 40 50 60 70 80 90 100

0 0.195 0.189 0.184 0.179 0.210 0.218 0.227 0.228 0.238 0.245 0.247 5 0.196 0.190 0.186 0.178 0.177 0.172 0.166 0.161 0.160 0.156 0.152 10 0.200 0.193 0.188 0.182 0.179 0.175 0.170 0.166 0.162 0.159 0.155 15 0.203 0.197 0.193 0.187 0.180 0.178 0.171 0.170 0.166 0.162 0.158 20 0.210 0.203 0.199 0.191 0.187 0.183 0.178 0.173 0.171 0.167 0.163 25 0.217 0.211 0.206 0.200 0.194 0.191 0.185 0.182 0.180 0.175 0.170 30 0.225 0.219 0.212 0.208 0.203 0.196 0.194 0.191 0.187 0.182 0.178

Table 2.7 Cm values for various configurations.

0 10 20 30 40 50 60 70 80 90 100

0 -0.32 -0.32 -0.32 -0.31 -0.32 -0.31 -0.31 -0.31 -0.32 -0.32 -0.31 5 -0.31 -0.31 -0.31 -0.31 -0.31 -0.31 -0.31 -0.31 -0.31 -0.31 -0.31 10 -0.38 -0.44 -0.38 -0.39 -0.39 -0.42 -0.43 -0.43 -0.43 -0.45 -0.45 15 -0.44 -0.48 -0.43 -0.44 -0.45 -0.46 -0.47 -0.49 -0.50 -0.51 -0.52 20 -0.49 -0.52 -0.46 -0.47 -0.48 -0.50 -0.51 -0.53 -0.51 -0.53 -0.53 25 -0.52 -0.54 -0.49 -0.51 -0.50 -0.50 -0.52 -0.54 -0.55 -0.55 -0.55 30 -0.53 -0.54 -0.54 -0.55 -0.55 -0.55 -0.56 -0.57 -0.57 -0.56 -0.58

Cm is defined as the change in pitching moment with respect to the angle of attack, for a stable aircraft this aero coefficient is negative. Cmq, also known as pitch damping, is the change in pitch moment with respect to the pitch rate. This is mainly a damping effect from the tail. As the aircraft pitched up, for example, the tail rotates downward relative to the CG. This increases the angle of attack of the horizontal tail, which generates a lift increment, which in turn generates a downwards pitching moment opposing the direction of the pitch rate. Cme is the change in the pitching moment due to elevator control effort;

19

this is the change in lift due to elevator deflection CLe multiplied by the moment arm between the center of gravity of the aircraft and the horizontal tail.

Table 2.8 Cmq values for various configurations.

0 10 20 30 40 50 60 70 80 90 100

0 -15.0 -15.0 -15.0 -15.0 -15.0 -15.0 -15.0 -15.0 -15.0 -15.0 -14.9 5 -14.7 -14.5 -14.2 -14.0 -13.8 -13.6 -13.4 -13.2 -13.0 -12.9 -12.7 10 -14.7 -14.6 -14.2 -14.1 -13.9 -13.7 -13.5 -13.3 -13.1 -13.0 -12.9 15 -14.9 -14.7 -14.4 -14.2 -14.0 -13.8 -13.6 -13.5 -13.3 -13.1 -13.0 20 -15.2 -14.9 -14.6 -14.4 -14.2 -14.0 -13.8 -13.7 -13.4 -13.3 -13.1 25 -15.6 -15.3 -15.0 -14.8 -14.5 -14.4 -14.2 -14.1 -13.9 -13.8 -13.5 30 -17.0 -16.6 -16.3 -16.1 -15.8 -15.5 -15.3 -15.0 -14.8 -14.5 -14.3

Table 2.9 Cme values for various configurations.

0 10 20 30 40 50 60 70 80 90 100

0 -1.81 -1.77 -1.81 -1.80 -1.80 -1.80 -1.80 -1.80 -1.80 -1.80 -1.80 5 -1.78 -1.75 -1.72 -1.69 -1.66 -1.64 -1.61 -1.59 -1.57 -1.54 -1.52 10 -1.78 -1.75 -1.72 -1.69 -1.66 -1.64 -1.62 -1.59 -1.57 -1.55 -1.51 15 -1.78 -1.75 -1.72 -1.69 -1.67 -1.64 -1.62 -1.59 -1.57 -1.55 -1.52 20 -1.80 -1.77 -1.73 -1.71 -1.68 -1.65 -1.63 -1.60 -1.58 -1.55 -1.53 25 -1.81 -1.77 -1.74 -1.72 -1.69 -1.66 -1.63 -1.61 -1.56 -1.54 -1.53 30 -1.63 -1.59 -1.56 -1.53 -1.50 -1.48 -1.45 -1.44 -1.42 -1.40 -1.38

These values were then verified by classical hand calculations based on the formulas of longitudinal dynamic stability which calculate the aerodynamic coefficients based on the geometrical parameters of the design and aerodynamic properties obtained from the airfoil section [20]. The formulas and the results are mentioned below [21]:

CLq=2ηCLαtVH

St dCLt St CLδe= η = ηCLαtτ Sw dδe Sw

20

X X dε dε 2C C = C ( CG - ac) -ηC V (1- ) , = Lαw mα Lαw c c Lαt H dα dα πAR

l C = -2ηC V t mq Lαt H c

dC C =-ηV Lt = -ηV C τ mδe H dδe H Lαt

Here, Clα = lift curve slope of the infinite wing span

η = tail efficiency factor = 0.9

CLαt = lift curve slope of the horizontal tail

VH = tail volume = 0.6696

2 St = tail area = 0.75ft

2 SW = wing area = 3.5ft

τ = flap effectiveness factor [21] = 0.4

XCG = x-location of the CG

Xac = x-location of the aerodynamic center

AR = aspect ratio = 3.5

lt = distance between CG of tail to the CG of the aircraft = 2.75ft

The results obtained are compared to the surfaces results in Table 2.10. It can be seen that the coefficients, although different are of the same order of magnitude. Since the numbers obtained from both these methods are similar, it can be argued that these methods conform closely to the results that would be obtained in nature. Therefore, the use of aerodynamic coefficients can be validated.

21

Table 2.10 Comparison between Classical calculations and SURFACES values.

Classical SURFACES Calculations

CL 3.96 4.01 CLq 7.73 4.32

CLe 0.55 0.28 Cm -0.32 -0.52 Cmq -15 -11.88 Cme -1.81 -0.86

2.3 ANALYSIS

It can be noted that, with sweep and span variation, various patterns of change are observed in the longitudinal stability derivatives. Some of the results are mentioned below with plausible explanations for these effects. It should be noted here that all the analysis is based on changes in a longitudinal model.

2.3.1 CL coefficients

 CLo: Figure 2.3 shows that CLo increases with the increase in span. This trend is to

be expected as the increase in span causes an increase in the lifting surface area;

therefore greater lift is generated over the wing. Although this is only a

preliminary analysis, it would be interesting to observe how the wing tip vortices

interact while span is being increased in future iterations. The trend is reversed

when the wing is swept back (Figure 2.4); this can be attributed to the fact that the

wing is now at an angle to the incoming velocity, and therefore the component of

the relative wind that is normal to the leading edge is reduced which contributes

to the reduction of lift.

22

Figure 2.3 CLo trend for Span Change.

Figure 2.4 CLo trend for Sweep Change.

23

Figure 2.5 CL trend for Span Change.

Figure 2.6 CL trend for Sweep Change.

 CL: Figure 2.5 and 2.6 show a similar trend as the observed span and sweep

change in CLo. The lift curve slope increases as the span increases because the

aspect ratio is lowered as the wing becomes more slender. CL is inversely

24

2 b a0 proportional to the AR, AR= , CLa = 2 where a0 = experimental lift curve S 1+ (1+Ʈ) AR slope for two dimensional flow, AR = aspect ratio and (1+Ʈ) = the experimental or theoretical correction for non-elliptical wing loading [22]. Similar to the sweep change trend in CLo, CL decreases as the wing is swept back, this can be attributed again to the reduced component of velocity that is now normal to the wing leading edge.

Figure 2.7 CLe trend for Span Change.

25

Figure 2.8 CLe trend for Sweep Change.

 CLe: CLt (the lift increment provided by the horizontal tail when the elevator is

St deflected) is directly proportional to where Sw is the wing area and St is the area of Sw

the tail. Sw increases with increasing span and therefore causes a gradual decrease in

the lift (Figure 2.7) L=qSC , ∂L =qS ∂CL , as S increases ∂CL decreases. Changing L ∂δe ∂δe ∂δe

sweep makes the downwash stronger at the tail thereby increasing the oncoming wind

velocity, and hence an increase in the lift is observed with elevator deflection (Figure

2.8).

26

Figure 2.9 CLq trend for Span Change.

Figure 2.10 CLq trend for Sweep Change.

 CLq: is the change in lift coefficient in response to pitch rate which is mainly a

horizontal tail effect. When the aircraft has a positive (nose up) pitch rate, the

horizontal tail rotates downward relative to the CG this increases the angle of

27

attack of the horizontal tail, which increases the lift. As the wing span increases,

this coefficient decreases in large part because the increment in the aircraft lift

coefficient due to tail lift is proportional to St , the ratio of tail to wing surface Sw

area, which decreases as wing span increases. When sweep increases, CLq is seen

to increase (Figure 2.9) which is likely caused by the increase in lift at the tail due

to the increased downwash angle at the horizontal tail due to the close proximity

of the wing tips to the tail for the swept back configuration (Figure 2.10).

2.3.2 CD coefficients

Figure 2.11 CD trend for Span Change.

28

Figure 2.12 CD trend for Sweep Change.

 CD: There is a slight decrease in the drag when the span is increased (Figure

2.11), this trend is caused by the decrease in induced drag of the aircraft as the

aspect ratio is increased. An aircraft with infinite aspect ratio would theoretically

produce zero induced drag. Sweeping the wings back, on the contrary, provides

more area for wing tip vortices to form along the span of the wing, thus creating a

higher induced drag. This can be observed in Figure 2.12.

29

2.3.3 Cm coefficients

Figure 2.13 Cm trend for Span Change.

Figure 2.14 Cm trend for Sweep Change.

30

 Cm: Span change has very little effect on Cmas shown in Figure 2.13 but due

to the movement of the center of gravity of the aircraft while sweeping the wings

back there is an increase in the moment arm from the aerodynamic wing to the

CG, which generates a higher Cm as seen in Figure 2.14.

Figure 2.15 Cme trend for Span Change.

Figure 2.16 Cme trend for Sweep Change.

31

 Cme: There is a slight decrease in the pitch moment coefficient due to elevator

defection (Figure 2.15) while changing the span; this trend is in direct correlation

with CLe as Cme is the change in lift caused by elevator deflection multiplied by

the moment arm between the CG of the aircraft and the horizontal tail. Sweep

change (Figure 2.16), however, decreases Cme which can be described by the

change in the CG of the aircraft similar to the trend observed in Figure 2.8.

Figure 2.17 Cmq trend for Span Change.

32

Figure 2.18 Cmq trend for Sweep Change.

 Cmq: As can be observed in Figure 2.17, there is a steady decrease in the

magnitude of pitch damping due to change in span, which can be attributed to the

same trend as observed in CLq, since change in lift at the horizontal tail causes

change in the pitch moment about the center of gravity. The evident increase in

pitch damping while sweeping the wing back is due to the movement of the CG

and the aerodynamic center (static margin) further away from each other; this

causes the moment arm to increase, thereby increasing the magnitude of pitch

damping as the wing is swept back.

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CHAPTER 3: SIMULATION DEVELOPMENT AND CONTROL

DESIGN

The aerodynamic coefficients obtained from SURFACES of the 77 different configurations for every combination of sweep back and span changes were used to construct a look up table for the longitudinal coefficients. These tables were then used to simulate the changing dynamics of the aircraft during morphing. 6 degrees of freedom model was then built to simulate the non-linear dynamic equations of an aircraft. This

SIMULINK model was then modified to incorporate a linear trajectory of sweep and span morphing at desired rates. Data obtained from SURFACES for various configurations of the aircraft was interpolated to form data tables, these tables serve as a reference to the non-linear model. For every time step during change in sweep and/or span of the aircraft longitudinal aerodynamic coefficients referenced for those particular configurations are fed into the model in real time. This created a real time dynamic simulation used to study the change in the longitudinal modes of the UAV. A state feedback controller was then designed as a stability augmentation system to enable the aircraft to maintain altitude throughout the flight. This flow of the simulation can be observed in Figure 3.1.

34

Figure 3.1 Flowchart depicting the flow of the Simulation.

35

3.1 NON-LINEAR SIMULINK MODEL

A 6-degrees-of-freedom nonlinear aircraft Simulink model with modifications set up to simulate wing morphing was developed to study the dynamic response of the morphing aircraft. The aircraft dynamic model includes the nonlinear rigid body equations of motion which take the form; ẋ(t)=f (x(t), u(t), t) where the state vector is

T defined as x(t)= {u, v, w, p, q, r, ∅, θ, φ, XN, YE, ZD} and the control vector is defined as u(t) = {훿푒,훿푇,훿푎, 훿푟}. The nonlinear equations of model are represented by f which time is varying due to morphing. The longitudinal aerodynamic forces and moments are dependent on the wing morphing configuration. Aerodynamic data from obtained from

SURFACES is used to generate 2-D tables of aerodynamic coefficients as a function of sweep and span. The simulation then interpolates the aerodynamic data from these tables to compute the appropriate aero-coefficients for the current span and sweep of the vehicle. The model was configured to inculcate time variant change in the sweep and span morphing so that geometry could be varied in different time intervals, this would help us better understand the transient effects speed of morphing has on the dynamics of an MAV. A chart depicting the simulation process is provided in Figure 3.1.

Time varying morphing functions was incorporated into the Simulink model in order to independently vary the wing span and sweep in the simulation. For the studies performed in this thesis the sweep and span were varied as a linear function of time:

(b -b ) b=b + f o ∙t o T

( - ) = + f o ∙t o T

36

Where, b,  = current span/sweep

bo,o = initial span/sweep

푏푓, 푓 = final span/sweep

T = time taken to reach from initial to final morphing geometry

t = current time step

Note that these functions are designed so that the morphing rate can be varied as a parameter in the simulation. These morphing functions can be easily modified to model different morphing trajectories, such as quadratic morphing function. At each step, the span and sweep are input to the aerodynamic tables that were generated using

SURFACES data, as can be observed in Figure 3.1

3.2 DYNAMIC MODE ANALYSIS

Trim conditions for the aircraft are determined in order to make the aircraft fly straight and level, those values are further used to linearize the model at the trim. This process corresponds to finding the angle of attack, elevator deflection and thrust for which the aircraft attains a longitudinal equilibrium (i.e. longitudinal forces and moments sum to zero). The 3 longitudinal equilibrium conditions to be satisfied for level flight are as follows:

T +C QS sin(α) -C QS cos(α) -Wsin (α) = 0 0 Ltrim Dtrim

-C QS cos(α) -C QS sin(α) +Wcos(α) = 0 Ltrim Dtrim

C QSc = 0 mtrim

37

Where, C =C +C α+C δe Ltrim Lo Lα Lδe

C =C +C α+C δe Dtrim Do Dα Dδe

C = C +C α+C δe mtrim mo mα mδe

Q = dynamic pressure

S = wing area

c = wing chord

And α, δe and T0 are the angle of attack, elevator deflection and thrust respectively, these three equations are solved to obtain the three trim variables.

In order to study the dynamic stability of the morphing aircraft, the nonlinear dynamic model was linearized about the trim state corresponding to each of the 4 morphing configurations shown in Table 3.1-3.4. This process generated a family of linearized longitudinal models of the form:

∆Ẋ (t)=[A]∆X(t)+[B]∆U(t)

Where,

∆X ={∆u, ∆w, ∆q, ∆θ}T

∆U = {∆δe, ∆δT}

Note that the linearized state and control vectors (∆X, ∆U ) correspond to the change in the state and control vector from the equilibrium values ∆푋표,∆푈표. Only 4 longitudinal states were included in the linear model because the other 2 longitudinal

38

states, north position XN and altitude h, do not significantly affect the longitudinal dynamic stability. The A matrix below represents the linearized longitudinal state space

[A] matrix of the MAV which is composed of stability derivatives that are functions of the aerodynamic coefficients, aircraft geometry and flight conditions:

A = 푋푢 + 푇푢 Xw 푋푞 − 푊0 -gcos( 휃 )

푍푢 푍푊 푍푞 + 푢0 -gsin(휃)

1 − 푍푤̇ 1 − 푍푤̇ 1 − 푍푤̇ 1-Zẇ

푀푢 + 푀̅̅̅̅푤̅̇ . 푍푢 푀푤 + 푀̅̅̅̅푤̅̇ . 푍푤 푀푞 + 푀푤̇ .푍푞 + 푢0. 푀̅̅̅̅푤̅̇ -̅M̅̅̅w̅̇ . gsin(θ)

0 0 1 0

Here, Xu = change in forces in the x-direction w.r.t the forwards velocity

Tu = change in thrust w.r.t forward velocity

Xw = change in forces in the x-direction w.r.t the downward velocity

Xq = change in forces in the x-direction w.r.t the pitch rate

W0 = is the upwards velocity at trim

g = acceleration due to gravity

θ = pitch angle at trim

Zu = change in forces in the z-direction w.r.t the forwards velocity

Zw = change in forces in the z-direction w.r.t the downward velocity

푍푤̇ = change in forces in the z-direction w.r.t the downward acceleration

Zq = change in forces in the z-direction w.r.t the pitch rate

u0 = forward velocity at trim

39

Mu = change in moment w.r.t to the forward velocity

Mw = change in moment w.r.t to the downward velocity

Mq = change in moment w.r.t to the pitch rate

푀푤̇ = change in moment w.r.t to the downward acceleration

The Eigenvalues of the different static configurations were first calculated and analyzed; the results are reported in the Tables 3.1-3.4. The dynamic stability of the aircraft for each of the 4 morphing configurations can be analyzed by computing the eigenvalues of the corresponding A matrices. Eigenvalues are determined as the solution to the equation:

[λI-A]v=0

n n Where, for an NxN matrix A, {λi} i=1are the eigenvalues and {vi} i=1are the corresponding eigenvectors. Equation 1 has nontrivial solutions only when [λI-A] is non- invertible. This leads to the condition where det[λI-A] = 0, for an NxN matrix, solving this equation leads to an Nth order characteristic polynomial. The roots of this characteristic polynomial correspond to the N eigenvalues. The eigenvectors associated with each eigenvalue can be found by substituting the appropriate eigenvalue into equation mentioned above and solving for v.

For all 4 morphing configurations the longitudinal eigenvalues, which determine the dynamic response and stability of the linear system take the form of two complex conjugate pairs. These complex conjugate eigenvalues correspond to the classical short

40

period and long period (Phugoid) modes. The Phugoid mode is characterized by low frequency (long period) oscillations in forward velocity and altitude, which are driven by the exchange of kinetic energy and potential energy as the aircraft changes altitude. The short period mode corresponds to a higher frequency pitch oscillation. From Table 3.1-

3.4 we can infer that the Phugoid and Short period modes are stable for the 4 static morphing configurations. This stability is apparent because the real parts of the eigenvalues are all negative; indicating that the motion is decreasing in amplitude for both the modes.

Table 3.1 Eigenvalues of the Basic Configuration.

0 Span change 0 Sweep back ° Eigen Values Damping Frequency(rad/s)

Short -17 + 5.74i 0.95 18.00 Period -17 - 5.74i 0.95 18.00 -0.11 + 0.203i 0.48 0.23 Phugoid -0.11 - 0.203i 0.48 0.23

Table 3.2 Eigenvalues of Full Sweep Configuration.

0 Span change 30 Sweep back ° Eigen Values Damping Frequency(rad/s)

Short -17.7 + 5.92i 0.95 18.60 Period -17.7 - 5.92i 0.95 18.60 -0.101 + 0.232i 0.40 0.25 Phugoid -0.101 – 0.2321i 0.40 0.25

41

Table 3.3 Eigenvalues of Full Span Configuration.

100% Span change 0 Sweep back ° Eigen Values Damping Frequency(rad/s)

Short -16.4 + 6.58i 0.93 22.7 Period -16.4 - 6.58i 0.93 22.7 -0.102 + 0.246i 0.38 0.27 Phugoid -0.102 - 0.246i 0.38 0.27

Table 3.4 Eigenvalues of Full Span Full Sweep Configuration.

100% Span change 30° Sweep back

Eigen Values Damping Frequency(rad/s)

Short -19 + 8.09i 0.92 20.70 Period -19 - 8.09i 0.92 20.70 -0.11 + 0.267i 0.38 0.29 Phugoid -0.11 - 0.267i 0.38 0.29

Table 3.1 lists the Eigenvalues of the basic configuration with no morphing; the damping ratios of the short period and long period modes are 0.95 and 0.48 respectively.

When the wing is swept back to 30°, no significant change in the short period damping is observed whereas the long period damping decreases (Table 3.2). It can also be noted that sweep back induces an increase in the frequency of oscillation for both the long and the short period motions. This increase in damping and frequency can be attributed to the decrease in the aspect ratio of the wing. The comparison between the basic configuration and the full span configuration shows (Table 3.3) a slight change in the short period damping ratio and a significant decrease in the long period damping, while the

42

frequencies show incremental changes. Table 3.4 lists the eigenvalues, damping ratios and frequencies of the short period and long period modes of the extended span and full sweep back configuration.

Although SURFACES is a reliable preliminary analysis tool, the drag model obtained from the low Reynold’s number conditions can be erroneous. This can be observed while analyzing the modes of the aircraft. The high damping ratios and frequency indicate higher drag than would be observed for a conventional aircraft of this design. It was observed that increasing drag in the model caused the long period

(phugoid) Eigenvalues to move towards the real axis and eventually the imaginary part would vanish with ample increase in drag. This caused the MAV to have a non- oscillatory long period motion with high damping.

3.3 CONTROLLER DESIGN

A longitudinal stability augmentation system (SAS) was designed to control the

MAV during morphing. Changing the wing span and/or sweep changes the trim conditions of the aircraft and, unless the system is altered by applying control inputs are applied, results in a change in altitude. The purpose of the SAS control system therefore was to enable the MAV to achieve constant-altitude trim conditions after morphing.

The SAS control system is designed as a state feedback controller ∆푈 = [−퐾]∆푋, here [K] is constant gain matrix. Substituting this control law into the linear state equation yields

∆Ẋ =[A]∆X+[B]∆U

=[A]∆X-[B] [K] ∆X

= [A-BK] ∆X

43

=[A] ∆X

The eigenvalues of [A] = [A-BK] determines the dynamic stability of the closed loop control system. The gain matrix K can be selected to place the eigenvalues of [A] to a set of desired values. For the longitudinal system, there are 4 states and 2 control inputs, resulting in a 2x4 gain matrix. The longitudinal SAS was designed to use only the elevator control input and not thrust. In addition, the longitudinal model was augmented to include a 5th altitude state h, which represents the change in altitude from the trim altitude. Therefore, with these modifications, the K matrix was of dimension 1x5.

The Bass-Gura method [21] was used to compute the gain matrix [K] based on a set of desired closed-loop eigenvalues, the following steps are followed:

 Eigenvalues are defined to achieve the desired modes of the system and the

desired characteristic polynomial was computed. By multiplying the Eigenvalues

of the system together. (휆) = ( 휆 − 휆1)( 휆 − 휆2)( 휆− 휆3)( 휆 − 휆4)( 휆 − 휆5)

5 4 3 2 = 휆 + 푎4휆 + 푎3휆 + 푎2휆 + 푎1휆+ 푎0

 The open loop characteristic polynomial is calculated as (λ) = det (λI-A)

 The controllability matrix is defined as [V] = [b| Ab| A2b|…|An-1b]. For this case

n=5 and b represents the column of the [B] matrix corresponding to the elevator.

 The gain matrix [K] is then computed by solving the following matrix operations:

T (([ ][ ])T)-1 T T [K] = V W (a̅-a), where a = {a4, a3, a2 , a1 , a0 } , a̅={a4, a3, a2, a1, ,a0}

and [W] is designed as an upper triangular 5x5 matrix with 1’s on the diagonal

44

and coefficients of the desired characteristic polynomials {a4, a3, a2 , a1 , a0 } on the

super diagonal.

In the nonlinear simulation model, the SAS is implemented as a feedback loop involving the forward velocity (u), altitude, vertical velocity (w), pitch rate (q) and pitch angle (θ). The required trim values are subtracted from the current simulation values to form an error vector {∆u, ∆w, ∆q, ∆θ, ∆h}T, which represents the deviation from the desired trim state. This error vector is then multiplied by the gain matrix [K] to obtain an elevator deflection, which is added to the trim elevator deflection for the corresponding to the desired trim state; this serves as the control effort outputted to the aircraft. SAS control systems were designed to drive the aircraft to full span trim condition and the full sweep trim condition. For example, the full span SAS implemented in the case where the aircraft morphs from the baseline (zero span increase, zero sweep angle) configuration to the full span configuration in order to trim the aircraft at the same altitude after the span change occurs.

3.4 SIMULATION RESULTS AND ANALYSIS

A series of simulation studies were performed in which the wing span and/or sweep were varied at different morphing rates. In each simulation the aircraft starts with the baseline configuration (i.e. zero span increase, zero sweep angle) at the calculated trim condition. The aircraft flies at this trim for the first 10 seconds of the simulation. The morphing starts at the 11th second and lasts till for a specified time depending on the morphing rate required. The altitude, angle of attack, total airspeed, pitch rate and pitch angle are then plotted v/s time for all the different morphing rates in order to analyze the

45

dynamics associated with morphing. Several open-loop morphing (i.e. no control system used) morphing cases are presented in order to demonstrate the effects of morphing.

Simulations results are then provided using the stability augmentation control system.

3.4.1 Open-loop Span change with Zero Sweep

The results obtained for span morphing at different rates are presented in Figures 3.2-3.6:

Altitude Change with Different Speeds of Morphing 900

800

700

600

500

Altitude (ft) 400 2 seconds 4 seconds 300 9 seconds 18 seconds 200 36 seconds

100 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.2 Altitude change for Span Morphing.

46

Change in Angle of Attack with different Speeds of Morphing 0.4

0.2

0

-0.2

(deg) -0.4

Angle ofAngle Attack -0.6 2 seconds 4 seconds 9 seconds -0.8 18 seconds 36 seconds

-1 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.3 Angle of Attack change for Span Morphing.

Airspeed Change with Different Speeds of Morphing 62

60 2 seconds 4 seconds 58 9 seconds 18 seconds 56 36 seconds 54

52

50

Airspeed (ft/s) 48

46

44

42 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.4 Airspeed change for Span Morphing.

47

Pitch Rate Change with Different Speeds of Morphing 2

1.5

1

0.5

0

(deg/sec) Pitch RatePitch 2 seconds -0.5 4 seconds 9 seconds -1 18 seconds 36 seconds

-1.5 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.5 Pitch Rate change for Span Morphing.

Pitch Angle Change with different speeds of Morphing 9 2 seconds 8 4 seconds 7 9 seconds 18 seconds 6 36 seconds 5

4

Pitch

(deg) 3

2

1

0

-1 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.6 Pitch Angle change for Span Change.

Increasing the span, as discussed in the previous sections, causes an increase in the total lift generated by the aircraft. Figure 3.2 plots the change in altitude v/s time while span changes. The morphing begins at the 11th second and continues for 2, 4, 9, 18 and 36 seconds. These five cases are plotted against each other to observe the trend. It

48

can be seen that the aircraft finds a new trim in climb after the span has changed; it is interesting to note that the rate of climb is not affected by the speed of morphing although the slower morphing cases trim into the climb with a delay thus creating a slight offset.

Figure 3.3 plots the angle of attack change v/s time, from which it is evident that oscillatory motion occurs in the faster cases. It can also be observed that the faster morphing cases cause the larger amplitude of oscillations; this is an important fact to consider as a more stable flight can be achieved with larger morphing durations as almost all the different cases damp out at about the same time. Figure 3.4 plots the Airspeed change for the span change, the same trends as angle of attack can be observed. The airspeed trims at a lower value than the initial trim; this is because the aircraft is now in a climbing trim condition. Similar trends are observed pitch rate (Figure 3.5) and pitch angle (Figure 3.6) although the pitch rate dampens out to zero while the pitch angle settles to a positive angle corresponding to a climb.

3.4.2 Open-loop Sweep change with Zero Span increase

Figures 3.7-3.11 illustrate the simulation results for the case in which the wing is morphed into a full (30° sweep back) sweep configuration with no span change. Results provided for different morphing rates corresponding to 2, 4, 9, 18 and 36 seconds.

The morphing begins at the 11th second and continues for 2, 4, 9, 18 and 36 seconds. Sweep change decreases the overall lift of the aircraft; this can be observed in the plot representing Altitude change (Figure 3.7) for sweep change. The MAV finds a trim in descent as opposed to climb as in the previous (span morphing) case. These five cases are plotted against each other to observe the trend. It can be seen that the aircraft finds a trim in descent after the sweep has changed; it is interesting to note that the rate of

49

climb is not affected by the speed of morphing although the slower morphing cases trim into the descent with a delay thus creating a slight offset. The Angle of Attack trims to a higher value for all the different speeds in approximately the same amount of time

(Figure 3.8), however the airspeed (Figure 3.9) increases a little due to the trim found in descent, the trends appear to be consistent with the previous cases. Figure 3.10 and 3.11 depict the pitch rate and pitch angle respectively, it can be observed here that the pitch rate dampens to a zero value from a negative pitch rate. This results in a negative aircraft pitch angle to point down and finding a negative trim angle which corresponds to a descent trim condition.

Altitude Change for Different Speeds of Morphing 250 2 seconds 200 4 seconds 9 seconds 150 18 seconds 36 seconds 100

50

(ft)

Altitude 0

-50

-100

-150 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.7 Altitude Change for Sweep Morphing.

50

AoA Change with Different Speeds of Morphing 0.05 2 seconds 0 4 seconds 9 seconds -0.05 18 seconds 36 seconds -0.1

-0.15

(deg) -0.2

Angle ofAngle Attack -0.25

-0.3

-0.35 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.8 Angle of Attack change for Sweep Morphing.

Airspeed Change with Different Speeds of Morphing 62

61.5

61

60.5

60

59.5

59

Airspeed (ft/s) 2 seconds 58.5 4 seconds

58 9 seconds 18 seconds 57.5 36 seconds

57 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.9 Airspeed change for Sweep Morphing.

51

Pitch Rate Change with Different Speeds of Morphing 0.6

0.4

0.2

0

-0.2 2 seconds Pitch RatePitch (deg/s) -0.4 4 seconds 9 seconds -0.6 18 seconds 36 seconds

-0.8 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.10 Pitch Rate change for Sweep Morphing.

Pitch Change with Different Speeds of Morphing 1 2 seconds 0.5 4 seconds 9 seconds 0 18 seconds 36 seconds -0.5

-1

Pitch (deg)Pitch -1.5

-2

-2.5

-3 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.11 Pitch Angle change for Sweep Morphing.

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3.4.3 Open-loop Span and Sweep Morphing

A set of open-loop simulations were performed in which the span and sweep were changed at the same time at varying morphing rates, the results of which are presented in

Figures 3.12-3.16.

Expanding the span and sweeping the wings back brings about a few changes that are difficult to perceive without the dynamic simulations. The overall lift on the aircraft increases and the aircraft finds itself in a trim climb like the span only case, but in this instance the rate of climb (Figure 3.12) is much lower than the one in observed in the span only case (Figure 3.2). This observation can be attributed to the fact that while a span increase causes an increment in the lift of the aircraft, sweep negates that effect to a certain extent. The angle of attack increases slightly to a new trim value (Figure 3.13) while the airspeed settles to a trim value which is lower than the initial trim (Figure 3.14); it can also be observed that the airspeed trim for the sweep-span morphing case is less than one noted in the span only case. Pitch rate (Figure 3.15) and pitch angle (Figure

3.16) follow similar trends as the previous cases, the pitch rate dies down to zero while the pitch angle settles at a positive value indicating a nose up moment and therefore climb.

It may be observed that the parameters observed in the above simulations settle to a trim value almost within the same time frame, although it can be argued that the faster morphing cases has more time to achieve equilibrium than the slower morphing scenarios. This phenomenon merits further investigation.

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Altitude Change with Differnt Speeds of Morphing 450

400

350

300 Attitude (ft) 2 seconds 4 seconds 250 9 seconds 18 seconds 36 seconds

200 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.12 Altitude change for Sweep and Span Morphing.

AoA Change with Different Speeds of Morphing 0

-0.05

-0.1

-0.15

-0.2

-0.25 2 seconds 4 seconds -0.3 9 seconds

Angle ofAngle (deg)Attack -0.35 18 seconds 36 seconds

-0.4 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.13 Angle of Attack change for Sweep and Span Morphing.

54

Airspeed Change with Different Morphing Speeds 61 2 seconds 60 4 seconds 9 seconds 18 seconds 59 36 seconds

58

57

True Airspeed (ft/s)

56

55 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.14 Airspeed change for Sweep and Span Morphing.

Pitch Rate Change with Different Speeds of Morphing 1 2 seconds 4 seconds 9 seconds 18 seconds 0.5 36 seconds

0

Pitch RatePitch (deg/s)

-0.5 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.15 Pitch Rate change for Sweep and Span Morphing.

55

Pitch Change with Differnt Speeds of Morphing 3 2 seconds 2.5 4 seconds 9 seconds 18 seconds 2 36 seconds

1.5

1

Pitch (deg)Pitch

0.5

0

-0.5 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.16 Pitch Angle change for Sweep and Span Morphing.

3.4.4 Closed Loop Control Cases

Figure 3.17 depicts the controller implemented to hold the altitude to 200 ft. for the span morphing case; two separate scenarios were simulated for this report, morphing was completed in 9 seconds for both cases. The first case depicts starting the altitude hold after the span morphing has taken place, whereas the second case is using the altitude hold as soon as the morphing starts. It can be inferred that the amplitude of oscillations is considerably lowered when the control effort is applied as soon as the morphing starts.

Figure 3.18 is the implementation of the altitude hold for the sweep morphing case, the morphing time is kept the same at 9 seconds for the 0 to 30° sweep. The results obtained are similar to the ones observed in the span morphing scenario although the amplitude of oscillation in this case is slightly larger and damping takes a longer amount of time.

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Altitude Change with Conroller Implemented 225 controller after morph 220 controller while morphing

215

210

205

Altitude (ft) 200

195

190

185 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.17 Altitude Change during controlled Span Morphing.

Altitude Change with Controller Implemented 210 controller applied after morph 205 controller applied while morphing

200

195

190

Altitude (ft) 185

180

175

170 0 20 40 60 80 100 120 140 160 180 200 Time (sec)

Figure 3.18 Altitude Change during controlled Sweep Morphing.

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CHAPTER 4: CONCLUSIONS

The objective of the thesis was to design and analyze a variable sweep, variable span morphing MAV and study the transient characteristics morphing induces into the dynamics of the vehicle. The research was based on the idea that the morphing longitudinal dynamics could be modeled as a quasi-static system and the effects of rate of morphing could be analyzed. This would help decipher optimal rates and trajectories of morphing.

A carbon fiber reinforced Styrofoam model of a wing was constructed. This wing was then instrumented with sensors for static and dynamic pressure measurements and servo motor actuated mechanisms for varying the sweep and span of the aircraft were developed. It was then tested in the wind tunnel to obtain the pressure variation during morphing for different rates of sweep back and span increase. The static and dynamic data collected were then analyzed to plot the pressure variation. Unfortunately, the data collected were inconclusive for predicting the transient changes that take place during morphing. The failure of the experiments could be attributed to an unstable open wind tunnel with high degree of variation in the speeds of operation and the inability of the data acquisition system to acquire the output at the sensitivity required for a successful experiment. More details about the experimental design set up and testing is explained in

Appendix A.

A UAV model designed around the experimental wing was then modeled in a

Vortex Lattice Method solver named SURFACES. This software uses the user to input

58

geometrical parameters and weight distribution and creates panels that simulate the flow over the surface. This three dimensional VLM solver outputs various aircraft properties ranging from the moments and inertias to the center of gravity, neutral points and stick fixed static margin. The software also provides us with aerodynamic coefficients and trim solutions for a selected airspeed and altitude for any of the required axis. 77 different models were created in SURFACES to represent every permutation of sweep and span change between the initial and final span (with 0.06’ increments) and zero to 30° sweep back (with 5° increments). The longitudinal aerodynamic coefficients were reported and the trends for span and sweep change were analyzed.

6 degrees of freedom model was then built to simulate the non-linear dynamic equations of an aircraft. This SIMULINK model was then modified to incorporate a linear trajectory of sweep and span morphing at desired rates. Data obtained from

SURFACES for various configurations of the aircraft was interpolated to form data tables, these tables serve as a reference to the non-linear model. For every time step during change in sweep and/or span of the aircraft longitudinal aerodynamic coefficients referenced for those particular configurations are fed into the model in real time. This created a real time dynamic simulation used to study the change in the longitudinal modes of the UAV.

The trim elevator deflection, trim angle of attack and trim thrust for the 4 end configurations were calculated. The non-linear model was then linearized about these trim conditions and a dynamic mode analysis on the 4 end static configurations was then carried out (‘end configurations’ imply the configuration at which the aircraft starts/finishes morphing). The eigenvalues for the zero span change-zero sweep back,

59

zero span change-full sweep back, full span change-zero sweep back and full span change-30° sweep back were calculated and reported. Important dynamic data like the frequency and damping of the oscillations of the two major longitudinal dynamic modes i.e. the short period and the phugoid (long period) were reported and the effect of geometrical changes on these parameters was highlighted.

A state feedback controller was then designed as a stability augmentation system to enable the aircraft to maintain altitude throughout the flight. The Bass-Gura method was used to calculate a gain matrix which was used to place the eigenvalues of the closed loop system to optimum values desired. This gain matrix was then multiplied with the feedback state errors to calculate the elevator deflections to maintain a constant altitude.

These simulations were run for five different rates of morphing 2, 4,9,18 and 36 seconds respectively. The longitudinal parameters like the forward velocity, angle of attack, pitch rate, pitch angle and the altitude were plotted against time. The results were analyzed and important trends were noted and discussed.

The thesis was successfully able to analyze and report the behavior of longitudinal dynamics of a morphing aircraft with varying rates of change.

4.1 FUTURE SCOPE OF WORK

Although a substantial amount of work has been accomplished during the course of this thesis, the author would like to propose some future research on this topic that can be accomplished.

 Re-conducting the experiments with dynamic pressure sensors and a stable wind

tunnel to obtain the dynamic changes that take place during morphing.

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 Analyzing the results of the experiments and building the intermediary transient

equations for the change of aerodynamic coefficients.

 Studying different morphing trajectories like quadratic, parabolic etc., other than

the linear trajectory case analyzed in this report.

 Model the lateral dynamic coefficients to analyze what effect morphing has on the

coupled modes.

 Design a dynamic controller that actively computes the controller gains to control

the MAV.

 Creating a Linear Time Varying (LTV) model to conduct modal analysis on

morphing dynamics.

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APPENDIX A

A.1 DESIGN

The prototype wing is a simple rectangular wing design made from a GA (W)-1 airfoil. This section has a 12 inch chord length and a 21 inch base span. It is able to increase its span to 25 inches and experiments were conducted on sweep change of up to

30 degrees. This prototype is depicted in Figure A.1.

Figure A.1 Wing Prototype.

To get the steady flow at low Reynolds numbers a laminar flow airfoil was selected (GA (W)-1). It was then reinforced so that the flutter can be reduced to an acceptable value at the speeds of operation required. Monokote, used as skin for wings was tried, to reinforce the wing but was found to be too flimsy to hold the extended wing section for span change. It was then decided that carbon fiber reinforcement would be strong enough to suppress flutter and hold the extended wing.

62

The Styrofoam wing was built by the Imperial Foam and Insulation Mfr. by means of a hot wire CNC. A CAD model of the airfoil shape and the dimensions were provided and a Styrofoam model of the wing was obtained. Mounting units were drilled onto the wing for mounting it to the wind tunnel’s force balance. The Styrofoam wing was then treated with epoxy and cotton fiber slurry to help prevent the chances of epoxy being soaked into the Styrofoam during the reinforcement process. This process was repeated until a thin consistent layer of epoxy was obtained; the layer was left to settle for an hour. A 1:2 mixture of epoxy to hardener was used to treat a 4 layer thick (0, +45,-45,

90) weave of carbon fiber. Two methods were investigated during this reinforcement: reinforcing each side of the wing one at a time with two separate sheets of carbon fiber or doing both sides at the same time with a single sheet. Treating both wing sides at the same time gave a better finish to the final product as compared to doing it one at a time.

The final product obtained was sturdy and could withstand high winds and shear; it was also able to support the extended wing but the surface finish obtained was not satisfactory. Therefore, it was decided to try vacuum bagging with a porous peel ply to obtain a smoother overall finish. The wing model was covered with a thin layer of epoxy and a sheet of porous peel ply was set upon the epoxy. The wing was then sealed and a vacuum setup. The vacuum helped the excess epoxy to get soaked by the peel ply and give us an even finish. Although a smoother finish was obtained from the process the model still needed to be sanded rigorously to obtain as close to a perfect finish as possible, seven coats of polyurethane paint and more sanding was done. It was decided that sanding was a never ending loop and mutual consensus was reached when a certain level of finish was reached to stop sanding.

63

The next step in the building process was placing all the sensors on the wing, precise drilling was done through the chord of the wing for placement of the condenser microphones and pressure taps, twenty four holes were drilled in total. The next step was to drill holes through the span of the wing to channel the wires connected to the sensors.

This was a challenging step as the longest drill bit available was 1 foot in length and the span wise length of the wing was 2.5 feet. A temporary design of two guiderails was set up to move the wing in the span wise direction without any lateral movement and a drilling machine was set up to on a carjack to support translation. The wing was slowly moved into the drill to achieve a tube like hole through the wing for the wires. Each condenser microphone and pressure tube was then wired into place.

To test the aerodynamic response of the morphing wing at different morphing speeds, the mechanisms responsible for operating the morphing of the wing must be able to change its activation speed when required. Therefore, both of the mechanisms to change the span length and the sweep angle ware powered by a servo motor, as shown in

Figure A.2, connected to a tunable servo speed regulator that is able to change the speed of the servo rotation when tuned, as shown in Figure A.3. The motion of the servo is controlled by using a CCPM controller shown in Figure A.4. The speed regulator is tuned to a different speed after every experiment to obtain data at different speeds. Both the sweeping and span change mechanisms are operated by using the same electrical components, as shown in Figure A.4 below.

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Figure A.2 Hitec-645MG Figure A.3 Figure A.4 CCPM servo Ultra Torque Servo. Speed/Direction controller. Regulator.

A.2 METHODOLOGY

There were two primary sensors used, the pressure transducers and the condenser microphones. These two sensors were plugged into the National Instruments USB-6008

Data Acquisition Board. The condenser microphones purchased from Radio Shack operated with a 9V battery, a 100Ω resistor, and a 10mF capacitor. The sensitivity of the device is -64±2dB. The signal/noise recognition of the condenser microphone is 50dB minimum with a frequency response of 50-10,000Hz. The pressure transducers allow input of pressure from the pressure taps and output alternating current to the DAQ board.

Finally, the National Instruments USB-6008 Data Acquisition Board accommodates four channels of differential analog input channels, which allow for the adjustment of input ranges. The analog input resolution is 12 bits differential with a maximum sample rate of

10kS/s (aggregate). Available input ranges in differential mode are ±1V, ±1.25V, ±2V,

±2.5V, ±4V, ±5V, ±10V, and ±20V. It is important to note that if single-ended analog input is selected, 8 analog inputs are available but only a voltage input range of ±10V is available.

The goal of this experiment was to find a suitable morphing speed that would be optimal for sweep and span change. This was achieved by investigating the aerodynamic

65

properties of a morphing wing during the transition stage. An experimental procedure was devised for the wing model in the wind tunnel. Before placing the test subject into the wind tunnel to conduct experiments, a few tests were conducted to make sure that the test devices work perfectly and gave the desired results. Tufts were also used in this test to obtain the flow movement of the airfoil. All the flows were recorded using high-speed camera and playback was done slow motion.

Constant pressure was used to perform the calibrations; the pressure taps, which had constant pressure during calibration, were connected to the Data Acquisition (DAQ) board. For every pressure value, there were five values that were collected to ensure the consistency. It is important to note that the original plan of having twelve measurements of pressure and transient response along the chord of the wing had to be changed due to restrictions of the DAQ. Since there were only four channels available for adjusting the input range, four locations of pressure and transient response were chosen based on engineering judgment. Figure A.5 shows these four locations of measurement and the subsequent omitted locations.

66

1.5 Station 1 6, 1.24 8 Omitted Locations 4 Actual Locations 1 Station 4

0.5, 0.64 0.5 Station 7

location location (in) 0

- y 0 0.15, -0.24 2 4 6 8 10 12 -0.5 Station 10 6, -0.73 -1 Chord Location (in.)

Figure A.5 Pressure Transducer/Condenser Microphone Locations.

The experiment began with the positioning of the test subject in the wind tunnel in such a way that there was minimum interference. A full set of tests was performed with the test object static in the initial position and the outcome was checked for inconsistencies. Inconsistent or unreasonable results in the sample tests might occur because of the sensors, the recording equipment, or the mounting of the test object. If there were no inconsistent results from the sample tests, the experiment would proceed by running a full set of tests with the test subject using varying sweep or span at different angle of attack.

Experimental data was collected by varying the speed of sweep or span change at different angles of attack (AoA). These measurements or parameters were collected as pressure variation with respect to time. By using the pressure variation given by the pressure transducer, aerodynamic coefficients and stability derivatives were then obtained

67

by plotting these variables against time, these can be used to determine the transient characteristics brought about by morphing sweep and span separately.

A.3 RESULTS

First, the data from the Data Acquisition System (DAS) had to be compiled. Once this was complete, the transient response during morphing was examined using the two sets of data: pressure readings before and after morphing and the transient response readings from the condenser microphones. As mentioned earlier, only four stations were analyzed due to restrictions of the DAQ board.

A.3.1 Span Morphing

As stated before, for each angle of attack, five voltage measurements from the pressure transducers for pre-morph and post-morph were taken. An average voltage from the five samples was then taken. The pressure was then found by applying the respective linear function of pressure vs. voltage from the calibration for each pressure transducer.

The resultant pressure is surface pressure minus ambient pressure (P- P∞). These pressure values can be converted into the coefficient of pressure by using Eq. (1). Then, subtracting the post-morph to pre-morph pressure, the change in Cp can be found.

2∆P CP=5.2023 2 (1) ρ∞ 푉∞

where P is the surface pressure minus ambient pressure at a particular station as found

before (in.H2O), ∞ is density at ambient room temperature (70 °F) and pressure (33

3 in.H2O), which is 2.329E-3 slug/ft for the tests, and V∞ is the free stream velocity (25m/s

68

= 82.02ft/s). Note that the additional term is to convert obtained pressure from in.H2O to lb. /ft2.

Table A.7 Change in Coefficient of Pressure from Pre to Post Span Morph.

Angle of Station 1 Station 4 Station 7 Station 10 Attack CP CP CP CP 0° 0.0238 0.0800 0.0351 0.0431 2° 0.4629 0.0999 -0.3304 0.0049 4° 0.1732 -0.0030 -0.1647 -0.0281

It is then possible to use the pressure distribution given by XFOIL to map out an approximate change in pressure distribution between pre and post morph. XFOIL is a subsonic airfoil development system used for the analysis of airfoils at subsonic velocities. In order to obtain the approximate pressure distribution over the airfoil, the

Reynolds number must be calculated using Eq. (2).

V c Re = ∞ (2) ν where c is the characteristic length, in our case the chord length (1ft), and  is the kinematic viscosity at ambient room temperature (70 °F) and pressure (33 in.H2O), which is 1.64E-4 ft2/s for the tests. The Reynolds number during testing was therefore around

0.50 million. XFOIL also requires the Mach number which can be found using Eq. (3).

V M   a (3)

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where a is the speed of sound at ambient room temperature (1128 ft/s). Therefore, the

Mach number during testing was 0.073.

Using the values calculated above, XFOIL was used to calculate the pressure distribution along the airfoil for all three angles of attack using the viscous calculation option (See Appendix for XFOIL graphs). The coefficient of pressure values were then plotted on the pressure distribution calculated in XFOIL to see the correlation.

-2 -1.8 -1.6 -1.4 -1.2

-1 Cp -0.8 -0.6 XFOIL Cp -0.4 Distribution -0.2 0 2 4 6 8 10 12 0 Chord Location (in.)

Figure A.6 Results of Span Change at 0° AoA Plotted on XFOIL Pressure Distribution.

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-2.5 XFOIL Cp Distribution -2

-1.5

Cp -1

-0.5

0 2 4 6 8 10 12 0 Chord Location (in.)

Figure A.7 Results of Span Change at 2° AoA Plotted on XFOIL Pressure Distribution.

-3 XFOIL Cp Distribution -2.5

-2

-1.5 Cp

-1

-0.5 0 2 4 6 8 10 12 0 Chord Location (in.)

Figure A.8 Results of Span Change at 4° AoA Plotted on XFOIL Pressure Distribution.

Based on engineering judgment, the results should indicate a decrease in pressure

(overall shift up of the graph) at all locations since the elliptical lift distribution has

71

shifted from ending near the pressure locations to a point farther away from the pressure taps. This is represented perfectly for the zero angle of attack data; however, the data is inconsistent at the other angles of attack. In other words, the span change does not show a consistent change in pressure distribution. It can be concluded that possible sources of this error may be that the pressure transducer/DAQ board set-up is inadequate (possibly due to insufficient calibration) to provide accurate results, or that the variations in the open wind tunnel, with its fluctuations in speed and occasional gusts.

A.3.2 Sweep Morphing

Again, at each angle of attack, five voltage measurements from the pressure transducers for pre-morph and post-morph were taken. An average voltage from the five samples was then taken and the pressure was found by applying the respective linear function of pressure vs. voltage from the calibration for each pressure transducer. The resultant pressure is surface pressure minus ambient pressure (P-Pinf) which is denoted as

P in the tables below. These pressure values can be converted to coefficient of pressure by using Eq. (1) and change in coefficient of pressure can be found by subtracting post-morph from pre-morph data.

Table A. 8 Change in Coefficient of Pressure from Pre to Post Sweep Morph.

Angle of Station 1 Station 4 Station 7 Station 10 Attack CP CP CP CP 0° 0.1144 -0.0172 -0.0764 -0.0478 2° 0.3063 0.1054 -0.1835 0.0086 4° 0.0271 0.0080 0.0696 -0.0006

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It does not make sense to compare these pressure distribution changes in XFOIL since the geometry change is no longer 2-D. However, it is still feasible to plot these results to qualitatively view the change.

-2 Pre-Morph Data -1.9 Post Morph Data -1.8 Station 4 -1.7

-1.6 Station 1

-1.5 Cp -1.4 -1.3 -1.2 Station 7 -1.1 0 1 2 3 4 5 Station6 10 7 -1 Chord Location (in.)

Figure A.9 Graphical Representation of Pressure Change for Sweep Change at 0° AoA.

73

-2.5 Pre-Morph Data Post Morph Data -2 Station 1 Station 4

-1.5

Cp

-1 Station 10 Station 7 -0.5

0 1 2 3 4 5 6 7 0 Chord Location (in.)

Figure A.10 Graphical Representation of Pressure Change for Sweep Change at 2° AoA.

-2.5

Station 1 Station 4 -2

-1.5

Cp Station 10 -1 Station 7 Pre-Morph Data -0.5 Post Morph Data

0 1 2 3 4 5 6 7 0 Chord Location (in.)

Figure A.11 Graphical Representation of Pressure Change for Sweep Change at 4° AoA.

Again, the results are inconsistent. The pressure changes from pre-morph to post- morph have no correlation. Engineering judgment would predict an overall decrease in magnitude of the pressure distribution due to the velocity decrease at the local points

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since only a component of the normal velocity is acting along the wing surface. It can be concluded that the pressure transducer/DAQ board set-up is inadequate to provide accurate results or the variations in the open wind tunnel invalidate the results. Other error sources, as mentioned in the previous section and the conclusion section, may also corrupt the experimental results.

A.3.3 Condenser Microphone Results

Condenser microphones were used in the experiment for capturing the dynamic response of the morphing pressure change. This section deals with the synthesis of data obtained from the condenser microphones during the processes of sweep and span change. A condenser microphone works on the principle of capacitance, any vibrations produced change the capacitance of the circuit and to maintain a constant capacitance the voltage is varied. Voltage in this case is recorded by the means of a Data Acquisition board, which saves it on a drive for further analysis.

There were two sets of test runs where data were collected; each set of tests had three different variants with varying speeds. The list below shows the different tests that were performed:

 Span Change

o 0o Angle of Attack at 25m/s

o 2o Angle of Attack at 25m/s

o 4o Angle of Attack at 25m/s

 Sweep Change

o 0o Angle of Attack at 25m/s

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. Slow sweep change

. Snap sweep change

o 2o Angle of Attack at 25m/s

. Slow sweep change

. Snap sweep change

o 4o Angle of Attack at 25m/s

. Slow sweep change

. Snap sweep change

Multiple runs of these data sets were collected and were first visually inspected to locate any noticeable change. As can be observed from Fig. 17, although there is no easily discernable change noticed at around 3 seconds, there is a change in amplitude of the signal. A Power Spectral Density plot was obtained to find that there was a dominant frequency at 60 Hz with harmonics at 120 and 180 Hz respectively, which could be attributed to AC noise. To further investigate these data, the specific time period was cut and plotted; the data was then passed through a stop-band filter to eliminate the AC frequency and harmonics. A low pass filter was used to eliminate the unwanted high frequencies as it was determined that any transient pressure change would occur at relatively low frequencies close to the frequency of morphing. Figure A.12 illustrates the data signal obtained from these filters.

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CondenserCondenser Microphone Microphone1 Data 3.35

3.3

3.25 0 1 2 3 4 5 6 7 8 9 10

TimeCondenser Microphone2(sec) 0.8

0.75

0.7 0 1 2 3 4 5 6 7 8 9 10

TimeCondenser Microphone3(sec)

2.42 Amplitude (dB) Amplitude 2.4

2.38

2.36 0 1 2 3 4 5 6 7 8 9 10

TimeCondenser Microphone4(sec) 2.36

2.35

2.34

2.33 0 1 2 3 4 5 6 7 8 9 10 Time (sec)

Figure A.12 Snap Sweep at 4 Degrees AoA.

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Section of interest 0.845 STOPBAND FILTER LOWPASS FILTER 0.84

0.835

0.83

0.825

0.82

0.815

Amplitude (dB)

0.81

0.805

0.8

0.795 2 2.5 3 3.5 4 4.5 5 5.5 6 Time (seconds)

Figure A.13 Section of Interest Filtered.

Welch Power Spectral Density Estimate -65

-70

-75

-80

-85

-90

Power/frequency (dB/Hz) -95

-100

-105 0 50 100 150 200 250 300 350 400 450 500 Frequency (Hz)

Figure A.14 PSD of the High-Pass and Stop-Band Filter.

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Unfortunately, there are no substantial results that can be derived about the changes that occur during morphing from the obtained data. This stems from the fact that the DAQ board and condenser microphone combination used could not measure the minute changes in frequency which occur during the morphing transition. The NI USB-

6008 was programmed for the best input range; however if the data exceeded the input range, no data were collected, which resulted in setting the DAQ to a higher input range, which did not collect the data as desired. This particular setback was detrimental to the data obtained and the required frequencies could not be captured. Some other flaws in the experimental setup were noticed: the sensitivity of Condenser microphones to ambient noise such as capturing the AC current frequency (the pressure transducer had to be turned off during the data collection to avoid superimposition), flutter of the wing was another issue that needed to be addressed even with dampened hinges, the flutter was high enough to be captured by the microphones in the 5-15 Hz range. This was particularly interesting to decipher in the data, during sweep change the hinge provided a moment to the wing to sweep it against the hinge; although great care was taken to have straight rods connecting the servo to the wing, there was still a vertical force provided by the rod that induced peak flutter. This phenomenon can be observed right at the start of morphing around 3 seconds (Figure A.13) into the experiment. PSD plots of the data reveal dominant frequencies of around 13.7 Hz (Figure A.14), which could be attributed to flutter.

The author found that the wind tunnel used for experimentation was not stable enough for dynamic testing. There was dynamic response captured by the condenser microphones, but the cause of the change could have been either the changing velocity or

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the geometrical changes. The frequency of both of these changes was of the same order of magnitude; therefore no classifications could be made. Although this experiment was unsuccessful, the author firmly believes this method can be modified and used in future testing of this kind.

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Appendix B

Pressure Transducer 4 Calibration 4 3.5 3 2.5 2 1.5

Pressure (in.H2O) 1 y = 141.62x - 313.77 R² = 0.9996 0.5 0 2.21 2.215 2.22 2.225 2.23 2.235 2.24 2.245 2.25 Voltage

Figure B.1 Calibration of Pressure Transducer Used at Station 4.

Pressure Transducer 7 Calibration 4 3.5 3 2.5 2 1.5

Pressure (in.H2O) 1 y = 137.91x - 306.28 R² = 0.9994 0.5 0 2.215 2.22 2.225 2.23 2.235 2.24 2.245 2.25 2.255 Voltage

Figure B.2 Calibration of Pressure Transducer Used at Station 7.

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Pressure Transducer 10 Calibration 4.5 4

3.5 3 2.5 2 1.5

Pressure (in.H2O) 1 y = 131.19x - 292.19 R² = 0.9988 0.5 0 2.22 2.225 2.23 2.235 2.24 2.245 2.25 2.255 2.26 Voltage

Figure B.3 Calibration of Pressure Transducer Used at Station 10.

Controller Battery packs

Speed regulator

Connected to servo Figure B.4 Electronics.

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Table B. 9 Pressure Readings from Pre to Post Span Morph

Station 4 Station 7 Station 10 Angle of Station 1 Condition P P P Attack P (in.H2O) (in.H2O) (in.H2O) (in.H2O) 0° -2.1814 -2.6666 -2.4830 -1.8400 Pre-Morph 2° -2.5637 -2.7692 -2.0946 -1.8941 4° -3.0000 -2.9242 -1.8451 -1.9438 0° -2.2173 -2.7870 -2.5359 -1.9049 Post-Morph 2° -3.2608 -2.9196 -1.5971 -1.9014 4° -3.2608 -2.9196 -1.5971 -1.9014

Table B.10 Coefficient of Pressure from Pre to Post Span Morph

Angle of Station 1 Station 4 Station 7 Station 10 Condition Attack CP CP CP CP 0° -1.4486 -1.7708 -1.6489 -1.2219 Pre-Morph 2° -1.7025 -1.8389 -1.3910 -1.2578 4° -1.9922 -1.9419 -1.2253 -1.2908 0° -1.4724 -1.8508 -1.6840 -1.2650 Post-Morph 2° -2.1654 -1.9389 -1.0606 -1.2627 4° -2.1654 -1.9389 -1.0606 -1.2627

Table B.11 Pressure readings from Pre to Post Sweep Morph

Station 4 Station 7 Station 10 Angle of Station 1 Condition P P P Attack P (in.H2O) (in.H2O) (in.H2O) (in.H2O) 0° -2.1112 -2.6726 -2.4572 -1.8721 Pre-Morph 2° -2.4848 -2.6814 -2.0775 -1.8169 4° -2.9053 -2.8282 -1.6964 -1.8308 0° -2.2835 -2.6468 -2.3422 -1.8001 Post-Morph 2° -2.9460 -2.8402 -1.8012 -1.8299 4° -2.9460 -2.8402 -1.8012 -1.8299

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Table B.12 Coefficient of Pressure from Pre to Post Sweep Morph

Angle of Station 1 Station 4 Station 7 Station 10 Condition Attack CP CP CP CP 0° -1.4020 -1.7748 -1.6318 -1.2432 Pre-Morph 2° -1.6501 -1.7806 -1.3796 -1.2066 4° -1.9293 -1.8781 -1.1265 -1.2158 0° -1.5164 -1.7577 -1.5554 -1.1954 Post-Morph 2° -1.9564 -1.8861 -1.1961 -1.2152 4° -1.9564 -1.8861 -1.1961 -1.2152

Figure B.5 XFOIL CP at 0° AoA

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Figure B.6 XFOIL Pressure Distribution at 0° AoA

Figure B.7 XFOIL CP at 2° AoA

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Figure B.8 XFOIL Pressure Distribution at 2° AoA

Figure B.9 XFOIL CP at 4° AoA

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Figure B.10 XFOIL Pressure Distribution at 4° AoA

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